Cellwise robust and sparse principal component analysis

doi:10.1007/s11634-025-00656-3

Return

Cellwise robust and sparse principal component analysis

2025-11-01

Pia Pfeiffer *

Laura Vana-Gür

Peter Filzmoser

DOI：10.1007/s11634-025-00656-3

Original

Original request for help

Save

Abstract

En 中文

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The integration of a sparsity-inducing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} or elastic net penalty offers additional modeling flexibility. For the resulting challenging optimization problem, an algorithm based on Riemannian stochastic gradient descent is developed, with the advantage of being scalable to high-dimensional data, both in terms of many variables as well as observations. The resulting method is called SCRAMBLE (Sparse Cellwise Robust Algorithm for Manifold-based Learning and Estimation). Simulations reveal the superiority of this approach in the high-dimenstional setting in comparison to established methods, both in the casewise and cellwise robustness paradigms. Two applications from the field of tribology underline the advantages of a cellwise robust and sparse PCA method.

Keywords:

Cellwise outliers

Robust PCA

Sparse PCA

Manifold learning